Question

A market-research firm was hired to determine the percentage of people in a market area who would purchase a client’s magazine if a door-to-door sales campaign were undertaken. The firm stated that 40% would buy if contacted at home. Suppose the marketing company has tried the sales campaign at 300 randomly selected homes. (150–225 words, or 2–3 paragraphs)

• Assuming the market research was done properly and the 40% is representative, how many sales are expected if the publisher attempts to sell to 5,000 homes?
• If the market research was accurate, what is the probability that fewer than 100 individuals will buy? Use the normal approximation to the binomial.
• Suppose that the publisher actually sells the magazine to 70 people out of the 300 contacted. What would you conclude about the market research? About the campaign?

Answer 1

The the number of homes out of who will actually buy the magazine has follows Binomial distribution with
The PMF of is .

a)If , the expected value is

b)  The normal approximation to the binomial is

The required probability is

c) When 300 people are contacted, the average number of magazines sold is .

The actual magazines sold is only 70 which is far away from the average 120. The campaign is not effective.